LMFDB - Embedded newform 945.2.t.b.341.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(341,945)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 0, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("945.341");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.t (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 315)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			341.11
Character	$\chi$	$=$	945.341
Dual form			945.2.t.b.521.5

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.23569i q^{2} +0.473066 q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.47654 + 0.930987i) q^{7} +3.05595i q^{8} +O(q^{10})$	\(q+1.23569i q^{2} +0.473066 q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.47654 + 0.930987i) q^{7} +3.05595i q^{8} +(1.07014 - 0.617846i) q^{10} +(1.10058 + 0.635419i) q^{11} +(1.67710 + 0.968277i) q^{13} +(-1.15041 + 3.06024i) q^{14} -2.83008 q^{16} +(-0.676881 - 1.17239i) q^{17} +(-0.724595 - 0.418345i) q^{19} +(-0.236533 - 0.409687i) q^{20} +(-0.785182 + 1.35997i) q^{22} +(0.914519 - 0.527998i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-1.19649 + 2.07238i) q^{26} +(1.17157 + 0.440418i) q^{28} +(8.49399 - 4.90401i) q^{29} -2.24847i q^{31} +2.61479i q^{32} +(1.44872 - 0.836416i) q^{34} +(-0.432012 - 2.61024i) q^{35} +(-4.38029 + 7.58689i) q^{37} +(0.516945 - 0.895376i) q^{38} +(2.64653 - 1.52797i) q^{40} +(-3.47470 + 6.01835i) q^{41} +(3.63907 + 6.30306i) q^{43} +(0.520646 + 0.300595i) q^{44} +(0.652443 + 1.13006i) q^{46} +1.69463 q^{47} +(5.26652 + 4.61126i) q^{49} +(-1.07014 - 0.617846i) q^{50} +(0.793381 + 0.458059i) q^{52} +(0.148100 - 0.0855054i) q^{53} -1.27084i q^{55} +(-2.84505 + 7.56818i) q^{56} +(6.05984 + 10.4960i) q^{58} -9.77894 q^{59} -2.84883i q^{61} +2.77842 q^{62} -8.89123 q^{64} -1.93655i q^{65} +13.0901 q^{67} +(-0.320209 - 0.554619i) q^{68} +(3.22546 - 0.533834i) q^{70} +6.48936i q^{71} +(9.10680 - 5.25781i) q^{73} +(-9.37506 - 5.41269i) q^{74} +(-0.342781 - 0.197905i) q^{76} +(2.13406 + 2.59827i) q^{77} -16.0108 q^{79} +(1.41504 + 2.45092i) q^{80} +(-7.43683 - 4.29366i) q^{82} +(-4.56456 - 7.90605i) q^{83} +(-0.676881 + 1.17239i) q^{85} +(-7.78864 + 4.49677i) q^{86} +(-1.94181 + 3.36331i) q^{88} +(9.41641 - 16.3097i) q^{89} +(3.25197 + 3.95934i) q^{91} +(0.432628 - 0.249778i) q^{92} +2.09404i q^{94} +0.836690i q^{95} +(-8.14174 + 4.70063i) q^{97} +(-5.69810 + 6.50780i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 30 q^{4} - 15 q^{5} - 3 q^{7}+O(q^{10}) $ 30 * q - 30 * q^4 - 15 * q^5 - 3 * q^7	$ 30 q - 30 q^{4} - 15 q^{5} - 3 q^{7} + 3 q^{10} - 9 q^{11} - 12 q^{13} + 27 q^{14} + 42 q^{16} + 3 q^{17} + 15 q^{20} + 15 q^{22} - 15 q^{25} - 24 q^{26} + 27 q^{28} + 48 q^{34} + 6 q^{35} - 3 q^{37} + 30 q^{38} + 3 q^{40} + 18 q^{41} + 12 q^{43} - 15 q^{44} + 9 q^{46} + 60 q^{47} - 15 q^{49} - 3 q^{50} - 33 q^{52} + 30 q^{53} - 42 q^{56} - 30 q^{59} - 12 q^{62} - 138 q^{64} + 12 q^{67} + 21 q^{68} - 18 q^{70} + 6 q^{73} - 54 q^{74} - 54 q^{76} + 9 q^{77} + 24 q^{79} - 21 q^{80} + 6 q^{82} + 6 q^{83} + 3 q^{85} + 60 q^{86} - 48 q^{88} + 3 q^{89} + 15 q^{91} + 3 q^{92} + 36 q^{97} - 24 q^{98}+O(q^{100}) $ 30 * q - 30 * q^4 - 15 * q^5 - 3 * q^7 + 3 * q^10 - 9 * q^11 - 12 * q^13 + 27 * q^14 + 42 * q^16 + 3 * q^17 + 15 * q^20 + 15 * q^22 - 15 * q^25 - 24 * q^26 + 27 * q^28 + 48 * q^34 + 6 * q^35 - 3 * q^37 + 30 * q^38 + 3 * q^40 + 18 * q^41 + 12 * q^43 - 15 * q^44 + 9 * q^46 + 60 * q^47 - 15 * q^49 - 3 * q^50 - 33 * q^52 + 30 * q^53 - 42 * q^56 - 30 * q^59 - 12 * q^62 - 138 * q^64 + 12 * q^67 + 21 * q^68 - 18 * q^70 + 6 * q^73 - 54 * q^74 - 54 * q^76 + 9 * q^77 + 24 * q^79 - 21 * q^80 + 6 * q^82 + 6 * q^83 + 3 * q^85 + 60 * q^86 - 48 * q^88 + 3 * q^89 + 15 * q^91 + 3 * q^92 + 36 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			1.23569i			0.873766i	0.899518	+	0.436883i	$0.143918\pi$
$2$			1.23569i			0.873766i	−0.899518	+	0.436883i	$0.856082\pi$
$3$		0			0
$3$		0			0
$4$	0.473066			0.236533
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	2.47654	+	0.930987i	0.936045	+	0.351880i
$7$	2.47654	+	0.930987i	0.936045	+	0.351880i
$8$			3.05595i			1.08044i
$9$		0			0
$10$	1.07014	−	0.617846i	0.338408	−	0.195380i
$11$	1.10058	+	0.635419i	0.331837	+	0.191586i	0.656656	−	0.754190i	$-0.271970\pi$
$11$	1.10058	+	0.635419i	0.331837	+	0.191586i	−0.324820	+	0.945776i	$0.605304\pi$
$12$		0			0
$13$	1.67710	+	0.968277i	0.465145	+	0.268552i	0.714205	−	0.699936i	$-0.246788\pi$
$13$	1.67710	+	0.968277i	0.465145	+	0.268552i	−0.249060	+	0.968488i	$0.580122\pi$
$14$	−1.15041	+	3.06024i	−0.307461	+	0.817884i
$15$		0			0
$16$	−2.83008			−0.707519
$17$	−0.676881	−	1.17239i	−0.164168	−	0.284347i	0.772192	−	0.635390i	$-0.219161\pi$
$17$	−0.676881	−	1.17239i	−0.164168	−	0.284347i	−0.936359	+	0.351043i	$0.885827\pi$
$18$		0			0
$19$	−0.724595	−	0.418345i	−0.166233	−	0.0959749i	0.414575	−	0.910015i	$-0.363930\pi$
$19$	−0.724595	−	0.418345i	−0.166233	−	0.0959749i	−0.580809	+	0.814040i	$0.697264\pi$
$20$	−0.236533	−	0.409687i	−0.0528904	−	0.0916088i
$21$		0			0
$22$	−0.785182	+	1.35997i	−0.167401	+	0.289948i
$23$	0.914519	−	0.527998i	0.190690	−	0.110095i	−0.401615	−	0.915808i	$-0.631551\pi$
$23$	0.914519	−	0.527998i	0.190690	−	0.110095i	0.592306	+	0.805713i	$0.298218\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−1.19649	+	2.07238i	−0.234651	+	0.406428i
$27$		0			0
$28$	1.17157	+	0.440418i	0.221405	+	0.0832313i
$29$	8.49399	−	4.90401i	1.57729	−	0.910651i	0.582059	−	0.813146i	$-0.302247\pi$
$29$	8.49399	−	4.90401i	1.57729	−	0.910651i	0.995235	−	0.0975049i	$-0.0310862\pi$
$30$		0			0
$31$		−	2.24847i		−	0.403838i	−0.979402	−	0.201919i	$-0.935282\pi$
$31$		−	2.24847i		−	0.403838i	0.979402	−	0.201919i	$-0.0647177\pi$
$32$			2.61479i			0.462234i
$33$		0			0
$34$	1.44872	−	0.836416i	0.248453	−	0.143444i
$35$	−0.432012	−	2.61024i	−0.0730234	−	0.441211i
$36$		0			0
$37$	−4.38029	+	7.58689i	−0.720116	+	1.24728i	0.240837	+	0.970566i	$0.422578\pi$
$37$	−4.38029	+	7.58689i	−0.720116	+	1.24728i	−0.960953	+	0.276712i	$0.910755\pi$
$38$	0.516945	−	0.895376i	0.0838596	−	0.145249i
$39$		0			0
$40$	2.64653	−	1.52797i	0.418453	−	0.241594i
$41$	−3.47470	+	6.01835i	−0.542657	+	0.939909i	0.456094	+	0.889932i	$0.349248\pi$
$41$	−3.47470	+	6.01835i	−0.542657	+	0.939909i	−0.998750	+	0.0499771i	$0.984085\pi$
$42$		0			0
$43$	3.63907	+	6.30306i	0.554953	+	0.961208i	0.997907	+	0.0646631i	$0.0205973\pi$
$43$	3.63907	+	6.30306i	0.554953	+	0.961208i	−0.442954	+	0.896544i	$0.646069\pi$
$44$	0.520646	+	0.300595i	0.0784903	+	0.0453164i
$45$		0			0
$46$	0.652443	+	1.13006i	0.0961974	+	0.166619i
$47$	1.69463			0.247187			0.123593	−	0.992333i	$-0.460558\pi$
$47$	1.69463			0.247187			0.123593	+	0.992333i	$0.460558\pi$
$48$		0			0
$49$	5.26652	+	4.61126i	0.752361	+	0.658751i
$50$	−1.07014	−	0.617846i	−0.151341	−	0.0873766i
$51$		0			0
$52$	0.793381	+	0.458059i	0.110022	+	0.0635213i
$53$	0.148100	−	0.0855054i	0.0203431	−	0.0117451i	−0.489794	−	0.871838i	$-0.662928\pi$
$53$	0.148100	−	0.0855054i	0.0203431	−	0.0117451i	0.510137	+	0.860093i	$0.329595\pi$
$54$		0			0
$55$		−	1.27084i		−	0.171360i
$56$	−2.84505	+	7.56818i	−0.380186	+	1.01134i
$57$		0			0
$58$	6.05984	+	10.4960i	0.795696	+	1.37819i
$59$	−9.77894			−1.27311			−0.636555	−	0.771232i	$-0.719641\pi$
$59$	−9.77894			−1.27311			−0.636555	+	0.771232i	$0.719641\pi$
$60$		0			0
$61$		−	2.84883i		−	0.364755i	−0.983229	−	0.182378i	$-0.941621\pi$
$61$		−	2.84883i		−	0.364755i	0.983229	−	0.182378i	$-0.0583793\pi$
$62$	2.77842			0.352860
$63$		0			0
$64$	−8.89123			−1.11140
$65$		−	1.93655i		−	0.240200i
$66$		0			0
$67$	13.0901			1.59921			0.799606	−	0.600525i	$-0.205042\pi$
$67$	13.0901			1.59921			0.799606	+	0.600525i	$0.205042\pi$
$68$	−0.320209	−	0.554619i	−0.0388311	−	0.0672574i
$69$		0			0
$70$	3.22546	−	0.533834i	0.385516	−	0.0638054i
$71$			6.48936i			0.770145i	0.922886	+	0.385072i	$0.125824\pi$
$71$			6.48936i			0.770145i	−0.922886	+	0.385072i	$0.874176\pi$
$72$		0			0
$73$	9.10680	−	5.25781i	1.06587	−	0.615380i	0.138820	−	0.990318i	$-0.455669\pi$
$73$	9.10680	−	5.25781i	1.06587	−	0.615380i	0.927050	+	0.374937i	$0.122336\pi$
$74$	−9.37506	−	5.41269i	−1.08983	−	0.629213i
$75$		0			0
$76$	−0.342781	−	0.197905i	−0.0393197	−	0.0227012i
$77$	2.13406	+	2.59827i	0.243199	+	0.296100i
$78$		0			0
$79$	−16.0108			−1.80136			−0.900679	−	0.434486i	$-0.856930\pi$
$79$	−16.0108			−1.80136			−0.900679	+	0.434486i	$0.856930\pi$
$80$	1.41504	+	2.45092i	0.158206	+	0.274021i
$81$		0			0
$82$	−7.43683	−	4.29366i	−0.821260	−	0.474155i
$83$	−4.56456	−	7.90605i	−0.501026	−	0.867802i	−0.999999	−	0.00118486i	$-0.999623\pi$
$83$	−4.56456	−	7.90605i	−0.501026	−	0.867802i	0.498974	−	0.866617i	$-0.333710\pi$
$84$		0			0
$85$	−0.676881	+	1.17239i	−0.0734181	+	0.127164i
$86$	−7.78864	+	4.49677i	−0.839871	+	0.484899i
$87$		0			0
$88$	−1.94181	+	3.36331i	−0.206997	+	0.358530i
$89$	9.41641	−	16.3097i	0.998138	−	1.72883i	0.446240	−	0.894913i	$-0.352763\pi$
$89$	9.41641	−	16.3097i	0.998138	−	1.72883i	0.551898	−	0.833912i	$-0.313904\pi$
$90$		0			0
$91$	3.25197	+	3.95934i	0.340899	+	0.415052i
$92$	0.432628	−	0.249778i	0.0451046	−	0.0260411i
$93$		0			0
$94$			2.09404i			0.215983i
$95$			0.836690i			0.0858426i
$96$		0			0
$97$	−8.14174	+	4.70063i	−0.826668	+	0.477277i	−0.852711	−	0.522384i	$-0.825043\pi$
$97$	−8.14174	+	4.70063i	−0.826668	+	0.477277i	0.0260423	+	0.999661i	$0.491710\pi$
$98$	−5.69810	+	6.50780i	−0.575595	+	0.657387i
$99$		0			0
$100$	−0.236533	+	0.409687i	−0.0236533	+	0.0409687i
$101$	−6.17344	+	10.6927i	−0.614280	+	1.06396i	0.376230	+	0.926526i	$0.377220\pi$
$101$	−6.17344	+	10.6927i	−0.614280	+	1.06396i	−0.990510	+	0.137438i	$0.956113\pi$
$102$		0			0
$103$	8.07033	−	4.65941i	0.795194	−	0.459105i	−0.0465942	−	0.998914i	$-0.514837\pi$
$103$	8.07033	−	4.65941i	0.795194	−	0.459105i	0.841788	+	0.539809i	$0.181503\pi$
$104$	−2.95900	+	5.12514i	−0.290154	+	0.502562i
$105$		0			0
$106$	0.105658	+	0.183006i	0.0102624	+	0.0177751i
$107$	−8.23320	−	4.75344i	−0.795934	−	0.459532i	0.0461137	−	0.998936i	$-0.485316\pi$
$107$	−8.23320	−	4.75344i	−0.795934	−	0.459532i	−0.842047	+	0.539404i	$0.818650\pi$
$108$		0			0
$109$	−3.22701	−	5.58935i	−0.309092	−	0.535363i	0.669072	−	0.743197i	$-0.266692\pi$
$109$	−3.22701	−	5.58935i	−0.309092	−	0.535363i	−0.978164	+	0.207835i	$0.933358\pi$
$110$	1.57036			0.149728
$111$		0			0
$112$	−7.00881	−	2.63477i	−0.662270	−	0.248962i
$113$	11.6622	+	6.73319i	1.09709	+	0.633405i	0.935455	−	0.353446i	$-0.114990\pi$
$113$	11.6622	+	6.73319i	1.09709	+	0.633405i	0.161635	+	0.986851i	$0.448323\pi$
$114$		0			0
$115$	−0.914519	−	0.527998i	−0.0852794	−	0.0492361i
$116$	4.01822	−	2.31992i	0.373082	−	0.215399i
$117$		0			0
$118$		−	12.0838i		−	1.11240i
$119$	−0.584842	−	3.53365i	−0.0536124	−	0.323929i
$120$		0			0
$121$	−4.69249	−	8.12762i	−0.426590	−	0.738875i
$122$	3.52027			0.318711
$123$		0			0
$124$		−	1.06368i		−	0.0955209i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−9.24610			−0.820459			−0.410229	−	0.911982i	$-0.634551\pi$
$127$	−9.24610			−0.820459			−0.410229	+	0.911982i	$0.634551\pi$
$128$		−	5.75724i		−	0.508873i
$129$		0			0
$130$	2.39298			0.209879
$131$	−6.24793	−	10.8217i	−0.545884	−	0.945499i	−0.998551	−	0.0538192i	$-0.982861\pi$
$131$	−6.24793	−	10.8217i	−0.545884	−	0.945499i	0.452667	−	0.891680i	$-0.350473\pi$
$132$		0			0
$133$	−1.40502	−	1.71064i	−0.121830	−	0.148331i
$134$			16.1753i			1.39734i
$135$		0			0
$136$	3.58277	−	2.06851i	0.307220	−	0.177373i
$137$	0.113595	+	0.0655839i	0.00970505	+	0.00560321i	0.504845	−	0.863210i	$-0.331550\pi$
$137$	0.113595	+	0.0655839i	0.00970505	+	0.00560321i	−0.495140	+	0.868813i	$0.664883\pi$
$138$		0			0
$139$	−3.27427	−	1.89040i	−0.277720	−	0.160342i	0.354671	−	0.934991i	$-0.384593\pi$
$139$	−3.27427	−	1.89040i	−0.277720	−	0.160342i	−0.632391	+	0.774650i	$0.717926\pi$
$140$	−0.204370	−	1.23482i	−0.0172724	−	0.104361i
$141$		0			0
$142$	−8.01884			−0.672927
$143$	1.23052	+	2.13133i	0.102901	+	0.178231i
$144$		0			0
$145$	−8.49399	−	4.90401i	−0.705387	−	0.407256i
$146$	6.49703	+	11.2532i	0.537698	+	0.931321i
$147$		0			0
$148$	−2.07217	+	3.58910i	−0.170331	+	0.295022i
$149$	−2.07964	+	1.20068i	−0.170371	+	0.0983635i	−0.582761	−	0.812644i	$-0.698027\pi$
$149$	−2.07964	+	1.20068i	−0.170371	+	0.0983635i	0.412390	+	0.911007i	$0.364694\pi$
$150$		0			0
$151$	−10.8621	+	18.8137i	−0.883946	+	1.53104i	−0.0370284	+	0.999314i	$0.511789\pi$
$151$	−10.8621	+	18.8137i	−0.883946	+	1.53104i	−0.846917	+	0.531725i	$0.821544\pi$
$152$	1.27844	−	2.21432i	0.103695	−	0.179605i
$153$		0			0
$154$	−3.21065	+	2.63704i	−0.258722	+	0.212499i
$155$	−1.94723	+	1.12424i	−0.156406	+	0.0903008i
$156$		0			0
$157$		−	12.2170i		−	0.975024i	−0.873116	−	0.487512i	$-0.837904\pi$
$157$		−	12.2170i		−	0.975024i	0.873116	−	0.487512i	$-0.162096\pi$
$158$		−	19.7844i		−	1.57397i
$159$		0			0
$160$	2.26448	−	1.30740i	0.179023	−	0.103359i
$161$	2.75641	−	0.456203i	0.217235	−	0.0359539i
$162$		0			0
$163$	8.73352	−	15.1269i	0.684062	−	1.18483i	−0.289668	−	0.957127i	$-0.593545\pi$
$163$	8.73352	−	15.1269i	0.684062	−	1.18483i	0.973731	−	0.227703i	$-0.0731216\pi$
$164$	−1.64376	+	2.84708i	−0.128356	+	0.222319i
$165$		0			0
$166$	9.76944	−	5.64039i	0.758256	−	0.437779i
$167$	3.83353	−	6.63987i	0.296648	−	0.513809i	−0.678719	−	0.734398i	$-0.737465\pi$
$167$	3.83353	−	6.63987i	0.296648	−	0.513809i	0.975367	+	0.220589i	$0.0707980\pi$
$168$		0			0
$169$	−4.62488	−	8.01053i	−0.355760	−	0.616194i
$170$	−1.44872	−	0.836416i	−0.111111	−	0.0641502i
$171$		0			0
$172$	1.72152	+	2.98176i	0.131265	+	0.227357i
$173$	16.0101			1.21722			0.608611	−	0.793469i	$-0.291727\pi$
$173$	16.0101			1.21722			0.608611	+	0.793469i	$0.291727\pi$
$174$		0			0
$175$	−2.04453	+	1.67925i	−0.154552	+	0.126940i
$176$	−3.11472	−	1.79828i	−0.234781	−	0.135551i
$177$		0			0
$178$	20.1538	+	11.6358i	1.51059	+	0.872139i
$179$	13.6009	−	7.85251i	1.01658	−	0.586924i	0.103470	−	0.994633i	$-0.467005\pi$
$179$	13.6009	−	7.85251i	1.01658	−	0.586924i	0.913112	+	0.407708i	$0.133672\pi$
$180$		0			0
$181$		−	6.50920i		−	0.483825i	−0.970298	−	0.241912i	$-0.922225\pi$
$181$		−	6.50920i		−	0.483825i	0.970298	−	0.241912i	$-0.0777747\pi$
$182$	−4.89253	+	4.01843i	−0.362658	+	0.297866i
$183$		0			0
$184$	1.61353	+	2.79472i	0.118951	+	0.206030i
$185$	8.76059			0.644091
$186$		0			0
$187$		−	1.72041i		−	0.125809i
$188$	0.801670			0.0584678
$189$		0			0
$190$	−1.03389			−0.0750063
$191$		−	9.33494i		−	0.675452i	−0.941244	−	0.337726i	$-0.890342\pi$
$191$		−	9.33494i		−	0.675452i	0.941244	−	0.337726i	$-0.109658\pi$
$192$		0			0
$193$	−5.60000			−0.403097			−0.201548	−	0.979479i	$-0.564597\pi$
$193$	−5.60000			−0.403097			−0.201548	+	0.979479i	$0.564597\pi$
$194$	−5.80854	−	10.0607i	−0.417029	−	0.722315i
$195$		0			0
$196$	2.49141	+	2.18143i	0.177958	+	0.155816i
$197$			7.13811i			0.508569i	0.967129	+	0.254284i	$0.0818400\pi$
$197$			7.13811i			0.508569i	−0.967129	+	0.254284i	$0.918160\pi$
$198$		0			0
$199$	9.64089	−	5.56617i	0.683425	−	0.394575i	−0.117719	−	0.993047i	$-0.537558\pi$
$199$	9.64089	−	5.56617i	0.683425	−	0.394575i	0.801144	+	0.598471i	$0.204225\pi$
$200$	−2.64653	−	1.52797i	−0.187138	−	0.108044i
$201$		0			0
$202$	−13.2129	−	7.62847i	−0.929656	−	0.536737i
$203$	25.6013	−	4.23718i	1.79686	−	0.297392i
$204$		0			0
$205$	6.94940			0.485367
$206$	5.75759	+	9.97244i	0.401151	+	0.694813i
$207$		0			0
$208$	−4.74634	−	2.74030i	−0.329099	−	0.190006i
$209$	−0.531648	−	0.920842i	−0.0367749	−	0.0636960i
$210$		0			0
$211$	4.41618	−	7.64904i	0.304022	−	0.526582i	−0.673021	−	0.739623i	$-0.735004\pi$
$211$	4.41618	−	7.64904i	0.304022	−	0.526582i	0.977043	+	0.213042i	$0.0683370\pi$
$212$	0.0700609	−	0.0404497i	0.00481180	−	0.00277810i
$213$		0			0
$214$	5.87379	−	10.1737i	0.401524	−	0.695460i
$215$	3.63907	−	6.30306i	0.248183	−	0.429865i
$216$		0			0
$217$	2.09330	−	5.56844i	0.142102	−	0.378010i
$218$	6.90671	−	3.98759i	0.467782	−	0.270074i
$219$		0			0
$220$		−	0.601190i		−	0.0405322i
$221$		−	2.62163i		−	0.176350i
$222$		0			0
$223$	7.09222	−	4.09470i	0.474930	−	0.274201i	−0.243371	−	0.969933i	$-0.578253\pi$
$223$	7.09222	−	4.09470i	0.474930	−	0.274201i	0.718301	+	0.695732i	$0.244920\pi$
$224$	−2.43434	+	6.47564i	−0.162651	+	0.432672i
$225$		0			0
$226$	−8.32014	+	14.4109i	−0.553448	+	0.958600i
$227$	−6.56772	+	11.3756i	−0.435915	+	0.755027i	−0.997370	−	0.0724804i	$-0.976909\pi$
$227$	−6.56772	+	11.3756i	−0.435915	+	0.755027i	0.561455	+	0.827507i	$0.310242\pi$
$228$		0			0
$229$	−9.67845	+	5.58785i	−0.639570	+	0.369256i	−0.784449	−	0.620194i	$-0.787054\pi$
$229$	−9.67845	+	5.58785i	−0.639570	+	0.369256i	0.144879	+	0.989449i	$0.453721\pi$
$230$	0.652443	−	1.13006i	0.0430208	−	0.0745142i
$231$		0			0
$232$	14.9864	+	25.9572i	0.983905	+	1.70417i
$233$	−14.3971	−	8.31218i	−0.943187	−	0.544549i	−0.0522289	−	0.998635i	$-0.516633\pi$
$233$	−14.3971	−	8.31218i	−0.943187	−	0.544549i	−0.890958	+	0.454086i	$0.849966\pi$
$234$		0			0
$235$	−0.847313	−	1.46759i	−0.0552726	−	0.0957350i
$236$	−4.62608			−0.301132
$237$		0			0
$238$	4.36650	−	0.722684i	0.283038	−	0.0468447i
$239$	14.4260	+	8.32885i	0.933140	+	0.538748i	0.887803	−	0.460223i	$-0.152231\pi$
$239$	14.4260	+	8.32885i	0.933140	+	0.538748i	0.0453365	+	0.998972i	$0.485564\pi$
$240$		0			0
$241$	−13.8667	−	8.00595i	−0.893233	−	0.515709i	−0.0182347	−	0.999834i	$-0.505805\pi$
$241$	−13.8667	−	8.00595i	−0.893233	−	0.515709i	−0.874999	+	0.484125i	$0.839138\pi$
$242$	10.0432	−	5.79847i	0.645604	−	0.372740i
$243$		0			0
$244$		−	1.34768i		−	0.0862766i
$245$	1.36021	−	6.86657i	0.0869004	−	0.438689i
$246$		0			0
$247$	−0.810148	−	1.40322i	−0.0515485	−	0.0892846i
$248$	6.87121			0.436322
$249$		0			0
$250$			1.23569i			0.0781520i
$251$	−14.7836			−0.933135			−0.466567	−	0.884486i	$-0.654509\pi$
$251$	−14.7836			−0.933135			−0.466567	+	0.884486i	$0.654509\pi$
$252$		0			0
$253$	1.34200			0.0843708
$254$		−	11.4253i		−	0.716889i
$255$		0			0
$256$	−10.6683			−0.666768
$257$	−3.84310	−	6.65644i	−0.239726	−	0.415217i	0.720910	−	0.693029i	$-0.243724\pi$
$257$	−3.84310	−	6.65644i	−0.239726	−	0.415217i	−0.960636	+	0.277812i	$0.910391\pi$
$258$		0			0
$259$	−17.9113	+	14.7113i	−1.11295	+	0.914113i
$260$		−	0.916118i		−	0.0568152i
$261$		0			0
$262$	13.3723	−	7.72051i	0.826145	−	0.476975i
$263$	−16.5237	−	9.53994i	−1.01889	−	0.588258i	−0.105109	−	0.994461i	$-0.533519\pi$
$263$	−16.5237	−	9.53994i	−1.01889	−	0.588258i	−0.913783	+	0.406203i	$0.866853\pi$
$264$		0			0
$265$	−0.148100	−	0.0855054i	−0.00909769	−	0.00525255i
$266$	2.11382	−	1.73617i	0.129607	−	0.106451i
$267$		0			0
$268$	6.19248			0.378266
$269$	−8.35391	−	14.4694i	−0.509347	−	0.882215i	−0.999941	−	0.0108266i	$-0.996554\pi$
$269$	−8.35391	−	14.4694i	−0.509347	−	0.882215i	0.490595	−	0.871388i	$-0.336780\pi$
$270$		0			0
$271$	−16.5843	−	9.57497i	−1.00743	−	0.581638i	−0.0969893	−	0.995285i	$-0.530921\pi$
$271$	−16.5843	−	9.57497i	−1.00743	−	0.581638i	−0.910437	+	0.413648i	$0.864255\pi$
$272$	1.91563	+	3.31796i	0.116152	+	0.201181i
$273$		0			0
$274$	−0.0810415	+	0.140368i	−0.00489590	+	0.00847994i
$275$	−1.10058	+	0.635419i	−0.0663673	+	0.0383172i
$276$		0			0
$277$	8.36521	−	14.4890i	0.502617	−	0.870558i	−0.497379	−	0.867533i	$-0.665704\pi$
$277$	8.36521	−	14.4890i	0.502617	−	0.870558i	0.999995	−	0.00302404i	$-0.000962584\pi$
$278$	2.33595	−	4.04599i	0.140101	−	0.242662i
$279$		0			0
$280$	7.97676	−	1.32021i	0.476703	−	0.0788975i
$281$	8.88850	−	5.13178i	0.530244	−	0.306136i	−0.210872	−	0.977514i	$-0.567630\pi$
$281$	8.88850	−	5.13178i	0.530244	−	0.306136i	0.741116	+	0.671377i	$0.234297\pi$
$282$		0			0
$283$			10.5602i			0.627737i	0.949466	+	0.313869i	$0.101625\pi$
$283$			10.5602i			0.627737i	−0.949466	+	0.313869i	$0.898375\pi$
$284$			3.06989i			0.182165i
$285$		0			0
$286$	−2.63366	+	1.52055i	−0.155732	+	0.0899118i
$287$	−14.2082	+	11.6698i	−0.838686	+	0.688847i
$288$		0			0
$289$	7.58366	−	13.1353i	0.446098	−	0.772664i
$290$	6.05984	−	10.4960i	0.355846	−	0.616344i
$291$		0			0
$292$	4.30811	−	2.48729i	0.252113	−	0.145558i
$293$	6.00652	−	10.4036i	0.350904	−	0.607784i	−0.635504	−	0.772098i	$-0.719208\pi$
$293$	6.00652	−	10.4036i	0.350904	−	0.607784i	0.986408	+	0.164314i	$0.0525409\pi$
$294$		0			0
$295$	4.88947	+	8.46881i	0.284676	+	0.493073i
$296$	−23.1851	−	13.3859i	−1.34761	−	0.778042i
$297$		0			0
$298$	−1.48367	−	2.56979i	−0.0859467	−	0.148864i
$299$	2.04499			0.118265
$300$		0			0
$301$	3.14425	+	18.9977i	0.181232	+	1.09501i
$302$	−23.2480	−	13.4222i	−1.33777	−	0.772362i
$303$		0			0
$304$	2.05066	+	1.18395i	0.117613	+	0.0679041i
$305$	−2.46716	+	1.42441i	−0.141269	+	0.0815617i
$306$		0			0
$307$			22.2161i			1.26794i	0.773358	+	0.633970i	$0.218576\pi$
$307$			22.2161i			1.26794i	−0.773358	+	0.633970i	$0.781424\pi$
$308$	1.00955	+	1.22915i	0.0575245	+	0.0700374i
$309$		0			0
$310$	−1.38921	−	2.40618i	−0.0789018	−	0.136662i
$311$	29.3734			1.66562			0.832808	−	0.553562i	$-0.186732\pi$
$311$	29.3734			1.66562			0.832808	+	0.553562i	$0.186732\pi$
$312$		0			0
$313$		−	29.8139i		−	1.68518i	−0.538553	−	0.842591i	$-0.681029\pi$
$313$		−	29.8139i		−	1.68518i	0.538553	−	0.842591i	$-0.318971\pi$
$314$	15.0965			0.851943
$315$		0			0
$316$	−7.57417			−0.426080
$317$			5.85984i			0.329121i	0.986367	+	0.164561i	$0.0526206\pi$
$317$			5.85984i			0.329121i	−0.986367	+	0.164561i	$0.947379\pi$
$318$		0			0
$319$	12.4644			0.697872
$320$	4.44562	+	7.70003i	0.248517	+	0.430445i
$321$		0			0
$322$	0.563727	+	3.40607i	0.0314153	+	0.189813i
$323$			1.13268i			0.0630240i
$324$		0			0
$325$	−1.67710	+	0.968277i	−0.0930290	+	0.0537103i
$326$	18.6922	+	10.7919i	1.03526	+	0.597710i
$327$		0			0
$328$	−18.3918	−	10.6185i	−1.01552	−	0.586308i
$329$	4.19682	+	1.57768i	0.231378	+	0.0869801i
$330$		0			0
$331$	−32.4278			−1.78239			−0.891195	−	0.453620i	$-0.850132\pi$
$331$	−32.4278			−1.78239			−0.891195	+	0.453620i	$0.850132\pi$
$332$	−2.15934	−	3.74008i	−0.118509	−	0.205264i
$333$		0			0
$334$	8.20484	+	4.73706i	0.448949	+	0.259201i
$335$	−6.54506	−	11.3364i	−0.357595	−	0.619372i
$336$		0			0
$337$	1.18605	−	2.05430i	0.0646084	−	0.111905i	−0.831912	−	0.554908i	$-0.812754\pi$
$337$	1.18605	−	2.05430i	0.0646084	−	0.111905i	0.896520	+	0.443003i	$0.146087\pi$
$338$	9.89854	−	5.71493i	0.538410	−	0.310851i
$339$		0			0
$340$	−0.320209	+	0.554619i	−0.0173658	+	0.0300784i
$341$	1.42872	−	2.47462i	0.0773696	−	0.134008i
$342$		0			0
$343$	8.74975	+	16.3230i	0.472442	+	0.881362i
$344$	−19.2618	+	11.1208i	−1.03853	+	0.599594i
$345$		0			0
$346$			19.7835i			1.06357i
$347$			30.4100i			1.63249i	0.577704	+	0.816246i	$0.303949\pi$
$347$			30.4100i			1.63249i	−0.577704	+	0.816246i	$0.696051\pi$
$348$		0			0
$349$	20.4722	−	11.8196i	1.09585	−	0.632690i	0.160723	−	0.987000i	$-0.448617\pi$
$349$	20.4722	−	11.8196i	1.09585	−	0.632690i	0.935128	+	0.354309i	$0.115284\pi$
$350$	−2.07504	−	2.52641i	−0.110916	−	0.135042i
$351$		0			0
$352$	−1.66149	+	2.87778i	−0.0885576	+	0.153386i
$353$	−5.32349	+	9.22056i	−0.283341	+	0.490761i	−0.972206	−	0.234129i	$-0.924776\pi$
$353$	−5.32349	+	9.22056i	−0.283341	+	0.490761i	0.688865	+	0.724890i	$0.258109\pi$
$354$		0			0
$355$	5.61995	−	3.24468i	0.298276	−	0.172210i
$356$	4.45458	−	7.71556i	0.236092	−	0.408924i
$357$		0			0
$358$	9.70328	+	16.8066i	0.512834	+	0.888255i
$359$	5.10095	+	2.94504i	0.269218	+	0.155433i	0.628532	−	0.777784i	$-0.283656\pi$
$359$	5.10095	+	2.94504i	0.269218	+	0.155433i	−0.359314	+	0.933217i	$0.616989\pi$
$360$		0			0
$361$	−9.14997	−	15.8482i	−0.481578	−	0.834117i
$362$	8.04336			0.422750
$363$		0			0
$364$	1.53839	+	1.87303i	0.0806338	+	0.0981734i
$365$	−9.10680	−	5.25781i	−0.476671	−	0.275206i
$366$		0			0
$367$	−0.666312	−	0.384696i	−0.0347812	−	0.0200810i	0.482509	−	0.875891i	$-0.339726\pi$
$367$	−0.666312	−	0.384696i	−0.0347812	−	0.0200810i	−0.517290	+	0.855810i	$0.673059\pi$
$368$	−2.58816	+	1.49427i	−0.134917	+	0.0778945i
$369$		0			0
$370$			10.8254i			0.562785i
$371$	0.446380	−	0.0738788i	0.0231749	−	0.00383560i
$372$		0			0
$373$	15.7575	+	27.2927i	0.815891	+	1.41316i	0.908686	+	0.417479i	$0.137086\pi$
$373$	15.7575	+	27.2927i	0.815891	+	1.41316i	−0.0927956	+	0.995685i	$0.529580\pi$
$374$	2.12590			0.109928
$375$		0			0
$376$			5.17869i			0.267071i
$377$	18.9937			0.978228
$378$		0			0
$379$	20.1303			1.03403			0.517013	−	0.855978i	$-0.327044\pi$
$379$	20.1303			1.03403			0.517013	+	0.855978i	$0.327044\pi$
$380$			0.395809i			0.0203046i
$381$		0			0
$382$	11.5351			0.590187
$383$	−10.6382	−	18.4259i	−0.543585	−	0.941517i	−0.998694	−	0.0510816i	$-0.983733\pi$
$383$	−10.6382	−	18.4259i	−0.543585	−	0.941517i	0.455109	−	0.890436i	$-0.349600\pi$
$384$		0			0
$385$	1.18313	−	3.14728i	0.0602981	−	0.160400i
$386$		−	6.91987i		−	0.352212i
$387$		0			0
$388$	−3.85158	+	2.22371i	−0.195534	+	0.112892i
$389$	−5.32769	−	3.07594i	−0.270124	−	0.155956i	0.358820	−	0.933407i	$-0.383179\pi$
$389$	−5.32769	−	3.07594i	−0.270124	−	0.155956i	−0.628944	+	0.777450i	$0.716513\pi$
$390$		0			0
$391$	−1.23804	−	0.714784i	−0.0626104	−	0.0361482i
$392$	−14.0918	+	16.0942i	−0.711742	+	0.812881i
$393$		0			0
$394$	−8.82050			−0.444370
$395$	8.00541	+	13.8658i	0.402796	+	0.697663i
$396$		0			0
$397$	−23.3539	−	13.4834i	−1.17210	−	0.676711i	−0.217924	−	0.975966i	$-0.569929\pi$
$397$	−23.3539	−	13.4834i	−1.17210	−	0.676711i	−0.954173	+	0.299255i	$0.903262\pi$
$398$	6.87807	+	11.9132i	0.344767	+	0.597153i
$399$		0			0
$400$	1.41504	−	2.45092i	0.0707519	−	0.122546i
$401$	−16.1812	+	9.34221i	−0.808050	+	0.466528i	−0.846278	−	0.532741i	$-0.821162\pi$
$401$	−16.1812	+	9.34221i	−0.808050	+	0.466528i	0.0382283	+	0.999269i	$0.487829\pi$
$402$		0			0
$403$	2.17714	−	3.77092i	0.108451	−	0.187843i
$404$	−2.92044	+	5.05836i	−0.145298	+	0.251663i
$405$		0			0
$406$	5.23585	+	31.6353i	0.259851	+	1.57003i
$407$	−9.64171	+	5.56664i	−0.477922	+	0.275928i
$408$		0			0
$409$			0.244490i			0.0120893i	0.999982	+	0.00604463i	$0.00192408\pi$
$409$			0.244490i			0.0120893i	−0.999982	+	0.00604463i	$0.998076\pi$
$410$			8.58731i			0.424097i
$411$		0			0
$412$	3.81780	−	2.20421i	0.188089	−	0.108594i
$413$	−24.2180	−	9.10407i	−1.19169	−	0.447982i
$414$		0			0
$415$	−4.56456	+	7.90605i	−0.224066	+	0.388093i
$416$	−2.53184	+	4.38528i	−0.124134	+	0.215006i
$417$		0			0
$418$	1.13788	−	0.656954i	0.0556554	−	0.0321327i
$419$	−14.3672	+	24.8847i	−0.701882	+	1.21569i	0.265923	+	0.963994i	$0.414323\pi$
$419$	−14.3672	+	24.8847i	−0.701882	+	1.21569i	−0.967805	+	0.251701i	$0.919010\pi$
$420$		0			0
$421$	−12.7923	−	22.1570i	−0.623460	−	1.07986i	−0.988837	−	0.149004i	$-0.952393\pi$
$421$	−12.7923	−	22.1570i	−0.623460	−	1.07986i	0.365377	−	0.930860i	$-0.380940\pi$
$422$	9.45186	+	5.45703i	0.460109	+	0.265644i
$423$		0			0
$424$	0.261300	+	0.452585i	0.0126898	+	0.0219795i
$425$	1.35376			0.0656671
$426$		0			0
$427$	2.65222	−	7.05525i	0.128350	−	0.341427i
$428$	−3.89485	−	2.24869i	−0.188264	−	0.108695i
$429$		0			0
$430$	7.78864	+	4.49677i	0.375602	+	0.216854i
$431$	5.46258	−	3.15382i	0.263123	−	0.151914i	−0.362635	−	0.931931i	$-0.618123\pi$
$431$	5.46258	−	3.15382i	0.263123	−	0.151914i	0.625758	+	0.780017i	$0.284790\pi$
$432$		0			0
$433$			0.0928113i			0.00446023i	0.999998	+	0.00223011i	$0.000709868\pi$
$433$			0.0928113i			0.00446023i	−0.999998	+	0.00223011i	$0.999290\pi$
$434$	6.88087	+	2.58667i	0.330292	+	0.124164i
$435$		0			0
$436$	−1.52659	−	2.64413i	−0.0731104	−	0.126631i
$437$	−0.883541			−0.0422655
$438$		0			0
$439$			12.2450i			0.584424i	0.956354	+	0.292212i	$0.0943912\pi$
$439$			12.2450i			0.584424i	−0.956354	+	0.292212i	$0.905609\pi$
$440$	3.88361			0.185144
$441$		0			0
$442$	3.23953			0.154089
$443$			35.8146i			1.70160i	0.525486	+	0.850802i	$0.323884\pi$
$443$			35.8146i			1.70160i	−0.525486	+	0.850802i	$0.676116\pi$
$444$		0			0
$445$	−18.8328			−0.892761
$446$	5.05978	+	8.76380i	0.239588	+	0.414978i
$447$		0			0
$448$	−22.0195	−	8.27762i	−1.04032	−	0.391081i
$449$			12.3951i			0.584960i	0.956272	+	0.292480i	$0.0944805\pi$
$449$			12.3951i			0.584960i	−0.956272	+	0.292480i	$0.905520\pi$
$450$		0			0
$451$	−7.64835	+	4.41578i	−0.360147	+	0.207931i
$452$	5.51700	+	3.18524i	0.259498	+	0.149821i
$453$		0			0
$454$	−14.0568	−	8.11568i	−0.659717	−	0.380888i
$455$	1.80291	−	4.79596i	0.0845216	−	0.224838i
$456$		0			0
$457$	−26.7109			−1.24948			−0.624742	−	0.780831i	$-0.714796\pi$
$457$	−26.7109			−1.24948			−0.624742	+	0.780831i	$0.714796\pi$
$458$	−6.90487	−	11.9596i	−0.322643	−	0.558834i
$459$		0			0
$460$	−0.432628	−	0.249778i	−0.0201714	−	0.0116459i
$461$	10.7493	+	18.6184i	0.500647	+	0.867146i	1.00000		0.000747358i	$0.000237891\pi$
$461$	10.7493	+	18.6184i	0.500647	+	0.867146i	−0.499353	+	0.866399i	$0.666429\pi$
$462$		0			0
$463$	8.69322	−	15.0571i	0.404008	−	0.699763i	−0.590197	−	0.807259i	$-0.700950\pi$
$463$	8.69322	−	15.0571i	0.404008	−	0.699763i	0.994205	+	0.107496i	$0.0342834\pi$
$464$	−24.0386	+	13.8787i	−1.11597	+	0.644303i
$465$		0			0
$466$	10.2713	−	17.7904i	0.475809	−	0.824125i
$467$	−14.2322	+	24.6509i	−0.658588	+	1.14071i	0.322393	+	0.946606i	$0.395513\pi$
$467$	−14.2322	+	24.6509i	−0.658588	+	1.14071i	−0.980981	+	0.194103i	$0.937821\pi$
$468$		0			0
$469$	32.4182	+	12.1867i	1.49693	+	0.562731i
$470$	1.81349	−	1.04702i	0.0836500	−	0.0482953i
$471$		0			0
$472$		−	29.8839i		−	1.37552i
$473$			9.24934i			0.425285i
$474$		0			0
$475$	0.724595	−	0.418345i	0.0332467	−	0.0191950i
$476$	−0.276669	−	1.67165i	−0.0126811	−	0.0766199i
$477$		0			0
$478$	−10.2919	+	17.8261i	−0.470740	+	0.815346i
$479$	−9.71758	+	16.8313i	−0.444007	+	0.769044i	−0.997982	−	0.0634898i	$-0.979777\pi$
$479$	−9.71758	+	16.8313i	−0.444007	+	0.769044i	0.553975	+	0.832533i	$0.313110\pi$
$480$		0			0
$481$	−14.6924	+	8.48268i	−0.669917	+	0.386777i
$482$	9.89289	−	17.1350i	0.450609	−	0.780477i
$483$		0			0
$484$	−2.21986	−	3.84490i	−0.100903	−	0.174768i
$485$	8.14174	+	4.70063i	0.369697	+	0.213445i
$486$		0			0
$487$	−2.99784	−	5.19242i	−0.135845	−	0.235291i	0.790075	−	0.613010i	$-0.210042\pi$
$487$	−2.99784	−	5.19242i	−0.135845	−	0.235291i	−0.925920	+	0.377720i	$0.876708\pi$
$488$	8.70587			0.394096
$489$		0			0
$490$	8.48497	+	1.68080i	0.383312	+	0.0759306i
$491$	−25.4050	−	14.6676i	−1.14651	−	0.661939i	−0.198478	−	0.980105i	$-0.563600\pi$
$491$	−25.4050	−	14.6676i	−1.14651	−	0.661939i	−0.948035	+	0.318166i	$0.896933\pi$
$492$		0			0
$493$	−11.4988	−	6.63886i	−0.517882	−	0.298999i
$494$	1.73394	−	1.00109i	0.0780138	−	0.0450413i
$495$		0			0
$496$			6.36335i			0.285723i
$497$	−6.04151	+	16.0712i	−0.270999	+	0.720890i
$498$		0			0
$499$	11.1595	+	19.3288i	0.499566	+	0.865274i	1.00000		0.000500987i	$-0.000159469\pi$
$499$	11.1595	+	19.3288i	0.499566	+	0.865274i	−0.500434	+	0.865775i	$0.666826\pi$
$500$	0.473066			0.0211561
$501$		0			0
$502$		−	18.2680i		−	0.815341i
$503$	−26.2714			−1.17139			−0.585693	−	0.810533i	$-0.699177\pi$
$503$	−26.2714			−1.17139			−0.585693	+	0.810533i	$0.699177\pi$
$504$		0			0
$505$	12.3469			0.549429
$506$			1.65830i			0.0737203i
$507$		0			0
$508$	−4.37401			−0.194066
$509$	−3.02895	−	5.24629i	−0.134256	−	0.232538i	0.791057	−	0.611742i	$-0.209531\pi$
$509$	−3.02895	−	5.24629i	−0.134256	−	0.232538i	−0.925313	+	0.379205i	$0.876198\pi$
$510$		0			0
$511$	27.4483	−	4.54288i	1.21424	−	0.200965i
$512$		−	24.6972i		−	1.09147i
$513$		0			0
$514$	8.22531	−	4.74888i	0.362803	−	0.209464i
$515$	−8.07033	−	4.65941i	−0.355621	−	0.205318i
$516$		0			0
$517$	1.86507	+	1.07680i	0.0820256	+	0.0473575i
$518$	−18.1786	−	22.1328i	−0.798721	−	0.972461i
$519$		0			0
$520$	5.91801			0.259522
$521$	1.55342	+	2.69061i	0.0680568	+	0.117878i	0.898046	−	0.439902i	$-0.144987\pi$
$521$	1.55342	+	2.69061i	0.0680568	+	0.117878i	−0.829989	+	0.557780i	$0.811653\pi$
$522$		0			0
$523$	18.9223	+	10.9248i	0.827417	+	0.477709i	0.852967	−	0.521964i	$-0.174801\pi$
$523$	18.9223	+	10.9248i	0.827417	+	0.477709i	−0.0255507	+	0.999674i	$0.508134\pi$
$524$	−2.95568	−	5.11939i	−0.129120	−	0.223642i
$525$		0			0
$526$	11.7884	−	20.4181i	0.514000	−	0.890273i
$527$	−2.63609	+	1.52195i	−0.114830	+	0.0662971i
$528$		0			0
$529$	−10.9424	+	18.9529i	−0.475758	+	0.824037i
$530$	0.105658	−	0.183006i	0.00458950	−	0.00794925i
$531$		0			0
$532$	−0.664665	−	0.809244i	−0.0288169	−	0.0350852i
$533$	−11.6549	+	6.72894i	−0.504828	+	0.291463i
$534$		0			0
$535$			9.50688i			0.411018i
$536$			40.0027i			1.72785i
$537$		0			0
$538$	17.8797	−	10.3229i	0.770849	−	0.445050i
$539$	2.86614	+	8.42150i	0.123453	+	0.362740i
$540$		0			0
$541$	2.01335	−	3.48723i	0.0865608	−	0.149928i	−0.819494	−	0.573087i	$-0.805746\pi$
$541$	2.01335	−	3.48723i	0.0865608	−	0.149928i	0.906055	+	0.423159i	$0.139079\pi$
$542$	11.8317	−	20.4931i	0.508215	−	0.880255i
$543$		0			0
$544$	3.06556	−	1.76990i	0.131435	−	0.0758840i
$545$	−3.22701	+	5.58935i	−0.138230	+	0.239421i
$546$		0			0
$547$	15.0541	+	26.0744i	0.643666	+	1.11486i	0.984608	+	0.174777i	$0.0559206\pi$
$547$	15.0541	+	26.0744i	0.643666	+	1.11486i	−0.340942	+	0.940084i	$0.610746\pi$
$548$	0.0537378	+	0.0310255i	0.00229556	+	0.00132534i
$549$		0			0
$550$	−0.785182	−	1.35997i	−0.0334803	−	0.0579895i
$551$	−8.20627			−0.349599
$552$		0			0
$553$	−39.6515	−	14.9059i	−1.68615	−	0.633862i
$554$	17.9039	+	10.3368i	0.760664	+	0.439169i
$555$		0			0
$556$	−1.54895	−	0.894284i	−0.0656899	−	0.0379261i
$557$	7.31014	−	4.22051i	0.309740	−	0.178829i	−0.337070	−	0.941480i	$-0.609436\pi$
$557$	7.31014	−	4.22051i	0.309740	−	0.178829i	0.646810	+	0.762651i	$0.276103\pi$
$558$		0			0
$559$			14.0945i			0.596135i
$560$	1.22263	+	7.38719i	0.0516655	+	0.312166i
$561$		0			0
$562$	6.34130	+	10.9834i	0.267491	+	0.463309i
$563$	9.89938			0.417209			0.208605	−	0.978000i	$-0.433108\pi$
$563$	9.89938			0.417209			0.208605	+	0.978000i	$0.433108\pi$
$564$		0			0
$565$		−	13.4664i		−	0.566535i
$566$	−13.0491			−0.548496
$567$		0			0
$568$	−19.8311			−0.832096
$569$		−	28.3984i		−	1.19052i	−0.803533	−	0.595261i	$-0.797049\pi$
$569$		−	28.3984i		−	1.19052i	0.803533	−	0.595261i	$-0.202951\pi$
$570$		0			0
$571$	13.2675			0.555229			0.277615	−	0.960693i	$-0.410456\pi$
$571$	13.2675			0.555229			0.277615	+	0.960693i	$0.410456\pi$
$572$	0.582118	+	1.00826i	0.0243396	+	0.0421574i
$573$		0			0
$574$	−14.4203	−	17.5570i	−0.601891	−	0.732816i
$575$			1.05600i			0.0440381i
$576$		0			0
$577$	−32.4703	+	18.7467i	−1.35176	+	0.780437i	−0.988495	−	0.151250i	$-0.951670\pi$
$577$	−32.4703	+	18.7467i	−1.35176	+	0.780437i	−0.363261	+	0.931687i	$0.618337\pi$
$578$	16.2312	+	9.37107i	0.675128	+	0.389785i
$579$		0			0
$580$	−4.01822	−	2.31992i	−0.166847	−	0.0963294i
$581$	−3.94389	−	23.8292i	−0.163620	−	0.988603i
$582$		0			0
$583$	0.217327			0.00900076
$584$	16.0676	+	27.8299i	0.664882	+	1.15161i
$585$		0			0
$586$	12.8556	+	7.42220i	0.531061	+	0.306608i
$587$	2.32671	+	4.02998i	0.0960337	+	0.166335i	0.910040	−	0.414521i	$-0.136051\pi$
$587$	2.32671	+	4.02998i	0.0960337	+	0.166335i	−0.814006	+	0.580857i	$0.802718\pi$
$588$		0			0
$589$	−0.940637	+	1.62923i	−0.0387583	+	0.0671313i
$590$	−10.4648	+	6.04188i	−0.430830	+	0.248740i
$591$		0			0
$592$	12.3966	−	21.4715i	0.509496	−	0.882473i
$593$	20.7205	−	35.8890i	0.850890	−	1.47379i	−0.0295154	−	0.999564i	$-0.509396\pi$
$593$	20.7205	−	35.8890i	0.850890	−	1.47379i	0.880406	−	0.474221i	$-0.157270\pi$
$594$		0			0
$595$	−2.76781	+	2.27331i	−0.113469	+	0.0931967i
$596$	−0.983805	+	0.568000i	−0.0402982	+	0.0232662i
$597$		0			0
$598$			2.52698i			0.103336i
$599$			26.6839i			1.09027i	0.838347	+	0.545137i	$0.183522\pi$
$599$			26.6839i			1.09027i	−0.838347	+	0.545137i	$0.816478\pi$
$600$		0			0
$601$	34.4248	−	19.8752i	1.40422	−	0.810726i	0.409396	−	0.912357i	$-0.365740\pi$
$601$	34.4248	−	19.8752i	1.40422	−	0.810726i	0.994822	+	0.101631i	$0.0324062\pi$
$602$	−23.4753	+	3.88532i	−0.956783	+	0.158354i
$603$		0			0
$604$	−5.13849	+	8.90013i	−0.209082	+	0.362141i
$605$	−4.69249	+	8.12762i	−0.190777	+	0.330435i
$606$		0			0
$607$	−39.0673	+	22.5555i	−1.58569	+	0.915500i	−0.591686	+	0.806168i	$0.701538\pi$
$607$	−39.0673	+	22.5555i	−1.58569	+	0.915500i	−0.994005	+	0.109331i	$0.965129\pi$
$608$	1.09388	−	1.89466i	0.0443629	−	0.0768388i
$609$		0			0
$610$	−1.76014	−	3.04865i	−0.0712659	−	0.123436i
$611$	2.84207	+	1.64087i	0.114978	+	0.0663824i
$612$		0			0
$613$	−0.0987025	−	0.170958i	−0.00398656	−	0.00690492i	0.864025	−	0.503448i	$-0.167936\pi$
$613$	−0.0987025	−	0.170958i	−0.00398656	−	0.00690492i	−0.868012	+	0.496544i	$0.834602\pi$
$614$	−27.4523			−1.10788
$615$		0			0
$616$	−7.94016	+	6.52157i	−0.319918	+	0.262762i
$617$	23.8582	+	13.7746i	0.960496	+	0.554543i	0.896326	−	0.443396i	$-0.146227\pi$
$617$	23.8582	+	13.7746i	0.960496	+	0.554543i	0.0641702	+	0.997939i	$0.479560\pi$
$618$		0			0
$619$	17.5302	+	10.1211i	0.704599	+	0.406800i	0.809058	−	0.587729i	$-0.199978\pi$
$619$	17.5302	+	10.1211i	0.704599	+	0.406800i	−0.104459	+	0.994529i	$0.533311\pi$
$620$	−0.921170	+	0.531838i	−0.0369951	+	0.0213591i
$621$		0			0
$622$			36.2965i			1.45536i
$623$	38.5043	−	31.6251i	1.54264	−	1.26703i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	36.8408			1.47246
$627$		0			0
$628$		−	5.77945i		−	0.230625i
$629$	11.8598			0.472879
$630$		0			0
$631$	18.5928			0.740166			0.370083	−	0.928999i	$-0.379329\pi$
$631$	18.5928			0.740166			0.370083	+	0.928999i	$0.379329\pi$
$632$		−	48.9282i		−	1.94626i
$633$		0			0
$634$	−7.24095			−0.287575
$635$	4.62305	+	8.00736i	0.183460	+	0.317762i
$636$		0			0
$637$	4.36754	+	12.8330i	0.173048	+	0.508463i
$638$			15.4021i			0.609777i
$639$		0			0
$640$	−4.98591	+	2.87862i	−0.197086	+	0.113787i
$641$	0.0435721	+	0.0251564i	0.00172100	+	0.000993617i	0.500860	−	0.865528i	$-0.333017\pi$
$641$	0.0435721	+	0.0251564i	0.00172100	+	0.000993617i	−0.499139	+	0.866522i	$0.666350\pi$
$642$		0			0
$643$	33.9516	+	19.6020i	1.33892	+	0.773026i	0.986647	−	0.162871i	$-0.0520755\pi$
$643$	33.9516	+	19.6020i	1.33892	+	0.773026i	0.352273	+	0.935897i	$0.385409\pi$
$644$	1.30396	−	0.215814i	0.0513833	−	0.00850427i
$645$		0			0
$646$	−1.39964			−0.0550682
$647$	−9.52565	−	16.4989i	−0.374492	−	0.648639i	0.615759	−	0.787935i	$-0.288850\pi$
$647$	−9.52565	−	16.4989i	−0.374492	−	0.648639i	−0.990251	+	0.139296i	$0.955516\pi$
$648$		0			0
$649$	−10.7625	−	6.21372i	−0.422464	−	0.243910i
$650$	−1.19649	−	2.07238i	−0.0469303	−	0.0812856i
$651$		0			0
$652$	4.13153	−	7.15602i	0.161803	−	0.280251i
$653$	−16.3324	+	9.42952i	−0.639136	+	0.369006i	−0.784282	−	0.620405i	$-0.786968\pi$
$653$	−16.3324	+	9.42952i	−0.639136	+	0.369006i	0.145145	+	0.989410i	$0.453635\pi$
$654$		0			0
$655$	−6.24793	+	10.8217i	−0.244127	+	0.422840i
$656$	9.83366	−	17.0324i	0.383940	−	0.665004i
$657$		0			0
$658$	−1.94952	+	5.18597i	−0.0760003	+	0.202170i
$659$	20.4698	−	11.8183i	0.797391	−	0.460374i	−0.0451672	−	0.998979i	$-0.514382\pi$
$659$	20.4698	−	11.8183i	0.797391	−	0.460374i	0.842558	+	0.538606i	$0.181049\pi$
$660$		0			0
$661$			49.0412i			1.90748i	0.300627	+	0.953742i	$0.402804\pi$
$661$			49.0412i			1.90748i	−0.300627	+	0.953742i	$0.597196\pi$
$662$		−	40.0707i		−	1.55739i
$663$		0			0
$664$	24.1605	−	13.9491i	0.937608	−	0.541329i
$665$	−0.778948	+	2.07210i	−0.0302063	+	0.0803525i
$666$		0			0
$667$	5.17861	−	8.96962i	0.200517	−	0.347305i
$668$	1.81351	−	3.14110i	0.0701669	−	0.121533i
$669$		0			0
$670$	14.0083	−	8.08767i	0.541186	−	0.312454i
$671$	1.81020	−	3.13536i	0.0698820	−	0.121039i
$672$		0			0
$673$	−4.36922	−	7.56772i	−0.168421	−	0.291714i	0.769444	−	0.638715i	$-0.220534\pi$
$673$	−4.36922	−	7.56772i	−0.168421	−	0.291714i	−0.937865	+	0.347000i	$0.887200\pi$
$674$	2.53848	+	1.46559i	0.0977787	+	0.0564526i
$675$		0			0
$676$	−2.18787	−	3.78951i	−0.0841489	−	0.145750i
$677$	7.92787			0.304693			0.152346	−	0.988327i	$-0.451317\pi$
$677$	7.92787			0.304693			0.152346	+	0.988327i	$0.451317\pi$
$678$		0			0
$679$	−24.5396	+	4.06146i	−0.941743	+	0.155865i
$680$	−3.58277	−	2.06851i	−0.137393	−	0.0793238i
$681$		0			0
$682$	3.05787	+	1.76546i	0.117092	+	0.0676029i
$683$	−2.95909	+	1.70843i	−0.113227	+	0.0653714i	−0.555544	−	0.831487i	$-0.687490\pi$
$683$	−2.95909	+	1.70843i	−0.113227	+	0.0653714i	0.442317	+	0.896859i	$0.354157\pi$
$684$		0			0
$685$		−	0.131168i		−	0.00501167i
$686$	−20.1703	+	10.8120i	−0.770104	+	0.412804i
$687$		0			0
$688$	−10.2989	−	17.8381i	−0.392640	−	0.680073i
$689$	0.331172			0.0126166
$690$		0			0
$691$			45.9833i			1.74929i	0.484767	+	0.874643i	$0.338904\pi$
$691$			45.9833i			1.74929i	−0.484767	+	0.874643i	$0.661096\pi$
$692$	7.57381			0.287913
$693$		0			0
$694$	−37.5773			−1.42642
$695$			3.78080i			0.143414i
$696$		0			0
$697$	9.40783			0.356347
$698$	14.6054	+	25.2973i	0.552823	+	0.957518i
$699$		0			0
$700$	−0.967197	+	0.794398i	−0.0365566	+	0.0300254i
$701$		−	30.4305i		−	1.14934i	−0.818384	−	0.574672i	$-0.805130\pi$
$701$		−	30.4305i		−	1.14934i	0.818384	−	0.574672i	$-0.194870\pi$
$702$		0			0
$703$	6.34788	−	3.66495i	0.239415	−	0.138226i
$704$	−9.78549	−	5.64965i	−0.368804	−	0.212929i
$705$		0			0
$706$	−11.3938	−	6.57820i	−0.428810	−	0.247574i
$707$	−25.2436	+	20.7336i	−0.949382	+	0.779766i
$708$		0			0
$709$	25.1986			0.946353			0.473177	−	0.880968i	$-0.343107\pi$
$709$	25.1986			0.946353			0.473177	+	0.880968i	$0.343107\pi$
$710$	4.00942	+	6.94452i	0.150471	+	0.260623i
$711$		0			0
$712$	49.8416	+	28.7761i	1.86789	+	1.07843i
$713$	−1.18719	−	2.05627i	−0.0444606	−	0.0770080i
$714$		0			0
$715$	1.23052	−	2.13133i	0.0460189	−	0.0797071i
$716$	6.43414	−	3.71476i	0.240455	−	0.138827i
$717$		0			0
$718$	−3.63916	+	6.30320i	−0.135812	+	0.235233i
$719$	−8.10824	+	14.0439i	−0.302386	+	0.523748i	−0.976676	−	0.214719i	$-0.931117\pi$
$719$	−8.10824	+	14.0439i	−0.302386	+	0.523748i	0.674290	+	0.738467i	$0.264450\pi$
$720$		0			0
$721$	24.3244	−	4.02585i	0.905887	−	0.149930i
$722$	19.5835	−	11.3065i	0.728823	−	0.420786i
$723$		0			0
$724$		−	3.07928i		−	0.114441i
$725$			9.80801i			0.364261i
$726$		0			0
$727$	37.7210	−	21.7782i	1.39899	−	0.807710i	0.404707	−	0.914446i	$-0.367373\pi$
$727$	37.7210	−	21.7782i	1.39899	−	0.807710i	0.994287	+	0.106736i	$0.0340401\pi$
$728$	−12.0995	+	9.93784i	−0.448439	+	0.368321i
$729$		0			0
$730$	6.49703	−	11.2532i	0.240466	−	0.416499i
$731$	4.92644	−	8.53284i	0.182211	−	0.315599i
$732$		0			0
$733$	−26.5351	+	15.3200i	−0.980096	+	0.565859i	−0.902299	−	0.431111i	$-0.858122\pi$
$733$	−26.5351	+	15.3200i	−0.980096	+	0.565859i	−0.0777969	+	0.996969i	$0.524789\pi$
$734$	0.475365	−	0.823357i	0.0175461	−	0.0303907i
$735$		0			0
$736$	1.38060	+	2.39128i	0.0508898	+	0.0881436i
$737$	14.4067	+	8.31770i	0.530677	+	0.306386i
$738$		0			0
$739$	13.5074	+	23.3956i	0.496879	+	0.860619i	0.999994	−	0.00360021i	$-0.00114598\pi$
$739$	13.5074	+	23.3956i	0.496879	+	0.860619i	−0.503115	+	0.864220i	$0.667813\pi$
$740$	4.14434			0.152349
$741$		0			0
$742$	0.0912914	+	0.551588i	0.00335141	+	0.0202494i
$743$	−21.9165	−	12.6535i	−0.804040	−	0.464213i	0.0408419	−	0.999166i	$-0.486996\pi$
$743$	−21.9165	−	12.6535i	−0.804040	−	0.464213i	−0.844882	+	0.534953i	$0.820329\pi$
$744$		0			0
$745$	2.07964	+	1.20068i	0.0761920	+	0.0439895i
$746$	−33.7254	+	19.4714i	−1.23478	+	0.712898i
$747$		0			0
$748$		−	0.813868i		−	0.0297580i
$749$	−15.9645	−	19.4371i	−0.583329	−	0.710216i
$750$		0			0
$751$	−18.1685	−	31.4687i	−0.662977	−	1.14831i	−0.979830	−	0.199835i	$-0.935960\pi$
$751$	−18.1685	−	31.4687i	−0.662977	−	1.14831i	0.316853	−	0.948475i	$-0.397374\pi$
$752$	−4.79592			−0.174889
$753$		0			0
$754$			23.4704i			0.854742i
$755$	21.7242			0.790625
$756$		0			0
$757$	11.5221			0.418778			0.209389	−	0.977832i	$-0.432853\pi$
$757$	11.5221			0.418778			0.209389	+	0.977832i	$0.432853\pi$
$758$			24.8749i			0.903496i
$759$		0			0
$760$	−2.55688			−0.0927478
$761$	−26.6098	−	46.0894i	−0.964603	−	1.67074i	−0.710678	−	0.703517i	$-0.751612\pi$
$761$	−26.6098	−	46.0894i	−0.964603	−	1.67074i	−0.253925	−	0.967224i	$-0.581722\pi$
$762$		0			0
$763$	−2.78822	−	16.8466i	−0.100940	−	0.609887i
$764$		−	4.41604i		−	0.159767i
$765$		0			0
$766$	22.7687	−	13.1455i	0.822666	−	0.474966i
$767$	−16.4003	−	9.46872i	−0.592181	−	0.341896i
$768$		0			0
$769$	3.95625	+	2.28414i	0.142666	+	0.0823682i	0.569634	−	0.821899i	$-0.307085\pi$
$769$	3.95625	+	2.28414i	0.142666	+	0.0823682i	−0.426968	+	0.904267i	$0.640418\pi$
$770$	3.88907	+	1.46199i	0.140152	+	0.0526864i
$771$		0			0
$772$	−2.64917			−0.0953456
$773$	1.60297	+	2.77642i	0.0576548	+	0.0998610i	0.893412	−	0.449238i	$-0.148304\pi$
$773$	1.60297	+	2.77642i	0.0576548	+	0.0998610i	−0.835757	+	0.549099i	$0.814971\pi$
$774$		0			0
$775$	1.94723	+	1.12424i	0.0699467	+	0.0403838i
$776$	−14.3649	−	24.8807i	−0.515669	−	0.893166i
$777$		0			0
$778$	3.80092	−	6.58338i	0.136269	−	0.236026i
$779$	5.03550	−	2.90725i	0.180415	−	0.104163i
$780$		0			0
$781$	−4.12346	+	7.14204i	−0.147549	+	0.255562i
$782$	0.883252	−	1.52984i	0.0315850	−	0.0547069i
$783$		0			0
$784$	−14.9047	−	13.0502i	−0.532310	−	0.466079i
$785$	−10.5802	+	6.10851i	−0.377625	+	0.218022i
$786$		0			0
$787$			1.94824i			0.0694472i	0.999397	+	0.0347236i	$0.0110551\pi$
$787$			1.94824i			0.0694472i	−0.999397	+	0.0347236i	$0.988945\pi$
$788$			3.37679i			0.120293i
$789$		0			0
$790$	−17.1338	+	9.89222i	−0.609594	+	0.351949i
$791$	22.6135	+	27.5324i	0.804043	+	0.978940i
$792$		0			0
$793$	2.75846	−	4.77778i	0.0979556	−	0.169664i
$794$	16.6613	−	28.8582i	0.591287	−	1.02414i
$795$		0			0
$796$	4.56078	−	2.63317i	0.161652	−	0.0933301i
$797$	17.4627	−	30.2462i	0.618559	−	1.07138i	−0.371190	−	0.928557i	$-0.621050\pi$
$797$	17.4627	−	30.2462i	0.618559	−	1.07138i	0.989749	−	0.142819i	$-0.0456166\pi$
$798$		0			0
$799$	−1.14706	−	1.98677i	−0.0405801	−	0.0702868i
$800$	−2.26448	−	1.30740i	−0.0800613	−	0.0462234i
$801$		0			0
$802$	−11.5441	−	19.9950i	−0.407636	−	0.706047i
$803$	13.3636			0.471593
$804$		0			0
$805$	−1.77329	−	2.15902i	−0.0625001	−	0.0760953i
$806$	4.65970	+	2.69028i	0.164131	+	0.0947610i
$807$		0			0
$808$	−32.6764	−	18.8657i	−1.14955	−	0.663693i
$809$	38.1558	−	22.0292i	1.34148	−	0.774507i	0.354460	−	0.935071i	$-0.384665\pi$
$809$	38.1558	−	22.0292i	1.34148	−	0.774507i	0.987025	+	0.160565i	$0.0513315\pi$
$810$		0			0
$811$		−	5.63536i		−	0.197884i	−0.995093	−	0.0989420i	$-0.968454\pi$
$811$		−	5.63536i		−	0.197884i	0.995093	−	0.0989420i	$-0.0315458\pi$
$812$	12.1111	−	2.00447i	0.425016	−	0.0703430i
$813$		0			0
$814$	−6.87865	−	11.9142i	−0.241097	−	0.417592i
$815$	−17.4670			−0.611844
$816$		0			0
$817$		−	6.08955i		−	0.213046i
$818$	−0.302115			−0.0105632
$819$		0			0
$820$	3.28752			0.114805
$821$		−	45.5736i		−	1.59053i	−0.606262	−	0.795265i	$-0.707332\pi$
$821$		−	45.5736i		−	1.59053i	0.606262	−	0.795265i	$-0.292668\pi$
$822$		0			0
$823$	−18.4733			−0.643938			−0.321969	−	0.946750i	$-0.604345\pi$
$823$	−18.4733			−0.643938			−0.321969	+	0.946750i	$0.604345\pi$
$824$	14.2389	+	24.6625i	0.496036	+	0.859159i
$825$		0			0
$826$	11.2498	−	29.9259i	0.391431	−	1.04126i
$827$			35.4707i			1.23344i	0.787184	+	0.616718i	$0.211538\pi$
$827$			35.4707i			1.23344i	−0.787184	+	0.616718i	$0.788462\pi$
$828$		0			0
$829$	7.87390	−	4.54600i	0.273472	−	0.157889i	−0.356992	−	0.934107i	$-0.616198\pi$
$829$	7.87390	−	4.54600i	0.273472	−	0.157889i	0.630464	+	0.776218i	$0.282864\pi$
$830$	−9.76944	−	5.64039i	−0.339102	−	0.195781i
$831$		0			0
$832$	−14.9115	−	8.60917i	−0.516964	−	0.298469i
$833$	1.84140	−	9.29571i	0.0638006	−	0.322077i
$834$		0			0
$835$	−7.66706			−0.265330
$836$	−0.251505	−	0.435619i	−0.00869847	−	0.0150662i
$837$		0			0
$838$	−30.7498	−	17.7534i	−1.06223	−	0.613280i
$839$	−3.86499	−	6.69435i	−0.133434	−	0.231115i	0.791564	−	0.611086i	$-0.209267\pi$
$839$	−3.86499	−	6.69435i	−0.133434	−	0.231115i	−0.924998	+	0.379971i	$0.875934\pi$
$840$		0			0
$841$	33.5986	−	58.1944i	1.15857	−	2.00670i
$842$	27.3792	−	15.8074i	0.943548	−	0.544758i
$843$		0			0
$844$	2.08914	−	3.61850i	0.0719113	−	0.124554i
$845$	−4.62488	+	8.01053i	−0.159101	+	0.275570i
$846$		0			0
$847$	−4.05442	−	24.4971i	−0.139312	−	0.841729i
$848$	−0.419134	+	0.241987i	−0.0143931	+	0.00830986i
$849$		0			0
$850$			1.67283i			0.0573777i
$851$			9.25114i			0.317125i
$852$		0			0
$853$	−30.8996	+	17.8399i	−1.05798	+	0.610827i	−0.924874	−	0.380274i	$-0.875830\pi$
$853$	−30.8996	+	17.8399i	−1.05798	+	0.610827i	−0.133110	+	0.991101i	$0.542496\pi$
$854$	8.71811	+	3.27733i	0.298328	+	0.112148i
$855$		0			0
$856$	14.5263	−	25.1602i	0.496497	−	0.859959i
$857$	−14.2012	+	24.5971i	−0.485102	+	0.840222i	−0.999853	−	0.0171176i	$-0.994551\pi$
$857$	−14.2012	+	24.5971i	−0.485102	+	0.840222i	0.514751	+	0.857340i	$0.327884\pi$
$858$		0			0
$859$	16.2603	−	9.38788i	0.554794	−	0.320310i	−0.196259	−	0.980552i	$-0.562879\pi$
$859$	16.2603	−	9.38788i	0.554794	−	0.320310i	0.751053	+	0.660242i	$0.229546\pi$
$860$	1.72152	−	2.98176i	0.0587034	−	0.101677i
$861$		0			0
$862$	3.89715	+	6.75006i	0.132737	+	0.229908i
$863$	20.0830	+	11.5949i	0.683634	+	0.394696i	0.801223	−	0.598366i	$-0.204183\pi$
$863$	20.0830	+	11.5949i	0.683634	+	0.394696i	−0.117589	+	0.993062i	$0.537517\pi$
$864$		0			0
$865$	−8.00503	−	13.8651i	−0.272179	−	0.471428i
$866$	−0.114686			−0.00389719
$867$		0			0
$868$	0.990269	−	2.63424i	0.0336119	−	0.0894119i
$869$	−17.6211	−	10.1736i	−0.597756	−	0.345115i
$870$		0			0
$871$	21.9535	+	12.6749i	0.743866	+	0.429471i
$872$	17.0808	−	9.86158i	0.578427	−	0.333955i
$873$		0			0
$874$		−	1.09178i		−	0.0369302i
$875$	2.47654	+	0.930987i	0.0837224	+	0.0314731i
$876$		0			0
$877$	23.6636	+	40.9866i	0.799064	+	1.38402i	0.920227	+	0.391386i	$0.128004\pi$
$877$	23.6636	+	40.9866i	0.799064	+	1.38402i	−0.121163	+	0.992633i	$0.538662\pi$
$878$	−15.1311			−0.510650
$879$		0			0
$880$			3.59657i			0.121240i
$881$	28.9064			0.973883			0.486941	−	0.873435i	$-0.338113\pi$
$881$	28.9064			0.973883			0.486941	+	0.873435i	$0.338113\pi$
$882$		0			0
$883$	−24.5641			−0.826648			−0.413324	−	0.910584i	$-0.635632\pi$
$883$	−24.5641			−0.826648			−0.413324	+	0.910584i	$0.635632\pi$
$884$		−	1.24021i		−	0.0417126i
$885$		0			0
$886$	−44.2559			−1.48680
$887$	13.9410	+	24.1465i	0.468092	+	0.810760i	0.999335	−	0.0364598i	$-0.0116081\pi$
$887$	13.9410	+	24.1465i	0.468092	+	0.810760i	−0.531243	+	0.847220i	$0.678275\pi$
$888$		0			0
$889$	−22.8984	−	8.60800i	−0.767986	−	0.288703i
$890$		−	23.2716i		−	0.780065i
$891$		0			0
$892$	3.35509	−	1.93706i	0.112337	−	0.0648576i
$893$	−1.22792	−	0.708939i	−0.0410907	−	0.0237237i
$894$		0			0
$895$	−13.6009	−	7.85251i	−0.454630	−	0.262481i
$896$	5.35992	−	14.2580i	0.179062	−	0.476328i
$897$		0			0
$898$	−15.3165			−0.511118
$899$	−11.0265	−	19.0985i	−0.367755	−	0.636971i
$900$		0			0
$901$	−0.200492	−	0.115754i	−0.00667935	−	0.00385632i
$902$	−5.45654	−	9.45100i	−0.181683	−	0.314684i
$903$		0			0
$904$	−20.5763	+	35.6391i	−0.684356	+	1.18534i
$905$	−5.63713	+	3.25460i	−0.187385	+	0.108187i
$906$		0			0
$907$	−5.04914	+	8.74536i	−0.167654	+	0.290385i	−0.937595	−	0.347730i	$-0.886952\pi$
$907$	−5.04914	+	8.74536i	−0.167654	+	0.290385i	0.769941	+	0.638115i	$0.220286\pi$
$908$	−3.10697	+	5.38142i	−0.103108	+	0.178589i
$909$		0			0
$910$	5.92633	+	2.22784i	0.196456	+	0.0738521i
$911$	4.94086	−	2.85261i	0.163698	−	0.0945111i	−0.415913	−	0.909404i	$-0.636538\pi$
$911$	4.94086	−	2.85261i	0.163698	−	0.0945111i	0.579611	+	0.814893i	$0.303205\pi$
$912$		0			0
$913$		−	11.6016i		−	0.383958i
$914$		−	33.0065i		−	1.09176i
$915$		0			0
$916$	−4.57854	+	2.64342i	−0.151279	+	0.0873412i
$917$	−5.39837	−	32.6172i	−0.178270	−	1.07712i
$918$		0			0
$919$	10.5866	−	18.3366i	0.349221	−	0.604869i	−0.636890	−	0.770955i	$-0.719780\pi$
$919$	10.5866	−	18.3366i	0.349221	−	0.604869i	0.986111	+	0.166086i	$0.0531128\pi$
$920$	1.61353	−	2.79472i	0.0531966	−	0.0921393i
$921$		0			0
$922$	−23.0066	+	13.2829i	−0.757683	+	0.437448i
$923$	−6.28349	+	10.8833i	−0.206824	+	0.358229i
$924$		0			0
$925$	−4.38029	−	7.58689i	−0.144023	−	0.249455i
$926$	18.6059	+	10.7421i	0.611429	+	0.353009i
$927$		0			0
$928$	12.8230	+	22.2100i	0.420934	+	0.729079i
$929$	2.90861			0.0954284			0.0477142	−	0.998861i	$-0.484806\pi$
$929$	2.90861			0.0954284			0.0477142	+	0.998861i	$0.484806\pi$
$930$		0			0
$931$	−1.88700	−	5.54452i	−0.0618439	−	0.181714i
$932$	−6.81079	−	3.93221i	−0.223095	−	0.128804i
$933$		0			0
$934$	−30.4609	−	17.5866i	−0.996712	−	0.575452i
$935$	−1.48992	+	0.860206i	−0.0487256	+	0.0281317i
$936$		0			0
$937$			0.261382i			0.00853898i	0.999991	+	0.00426949i	$0.00135902\pi$
$937$			0.261382i			0.00853898i	−0.999991	+	0.00426949i	$0.998641\pi$
$938$	−15.0590	+	40.0589i	−0.491695	+	1.30797i
$939$		0			0
$940$	−0.400835	−	0.694267i	−0.0130738	−	0.0226445i
$941$	12.2499			0.399336			0.199668	−	0.979864i	$-0.436014\pi$
$941$	12.2499			0.399336			0.199668	+	0.979864i	$0.436014\pi$
$942$		0			0
$943$			7.33853i			0.238976i
$944$	27.6751			0.900749
$945$		0			0
$946$	−11.4293			−0.371600
$947$		−	2.95899i		−	0.0961542i	−0.998844	−	0.0480771i	$-0.984691\pi$
$947$		−	2.95899i		−	0.0961542i	0.998844	−	0.0480771i	$-0.0153093\pi$
$948$		0			0
$949$	20.3641			0.661046
$950$	0.516945	+	0.895376i	0.0167719	+	0.0290498i
$951$		0			0
$952$	10.7986	−	1.78725i	0.349986	−	0.0579250i
$953$			17.5549i			0.568660i	0.958726	+	0.284330i	$0.0917711\pi$
$953$			17.5549i			0.568660i	−0.958726	+	0.284330i	$0.908229\pi$
$954$		0			0
$955$	−8.08429	+	4.66747i	−0.261602	+	0.151036i
$956$	6.82444	+	3.94009i	0.220718	+	0.127432i
$957$		0			0
$958$	−20.7983	−	12.0079i	−0.671964	−	0.387959i
$959$	0.220264	+	0.268177i	0.00711271	+	0.00865988i
$960$		0			0
$961$	25.9444			0.836915
$962$	−10.4820	−	18.1553i	−0.337952	−	0.585351i
$963$		0			0
$964$	−6.55987	−	3.78734i	−0.211279	−	0.121982i
$965$	2.80000	+	4.84974i	0.0901351	+	0.156119i
$966$		0			0
$967$	2.54007	−	4.39953i	0.0816832	−	0.141479i	−0.822290	−	0.569069i	$-0.807304\pi$
$967$	2.54007	−	4.39953i	0.0816832	−	0.141479i	0.903973	+	0.427589i	$0.140637\pi$
$968$	24.8376	−	14.3400i	0.798310	−	0.460905i
$969$		0			0
$970$	−5.80854	+	10.0607i	−0.186501	+	0.323029i
$971$	−25.6635	+	44.4505i	−0.823582	+	1.42649i	0.0794166	+	0.996842i	$0.474694\pi$
$971$	−25.6635	+	44.4505i	−0.823582	+	1.42649i	−0.902998	+	0.429644i	$0.858639\pi$
$972$		0			0
$973$	−6.34893	−	7.72996i	−0.203537	−	0.247811i
$974$	6.41623	−	3.70441i	0.205589	−	0.118697i
$975$		0			0
$976$			8.06240i			0.258071i
$977$		−	56.3370i		−	1.80238i	−0.433423	−	0.901191i	$-0.642694\pi$
$977$		−	56.3370i		−	1.80238i	0.433423	−	0.901191i	$-0.357306\pi$
$978$		0			0
$979$	20.7270	−	11.9667i	0.662437	−	0.382458i
$980$	0.643467	−	3.24834i	0.0205548	−	0.103764i
$981$		0			0
$982$	18.1246	−	31.3928i	0.578380	−	1.00178i
$983$	−23.1843	+	40.1564i	−0.739465	+	1.28079i	0.213272	+	0.976993i	$0.431588\pi$
$983$	−23.1843	+	40.1564i	−0.739465	+	1.28079i	−0.952737	+	0.303798i	$0.901745\pi$
$984$		0			0
$985$	6.18178	−	3.56905i	0.196968	−	0.113719i
$986$	8.20358	−	14.2090i	0.261255	−	0.452507i
$987$		0			0
$988$	−0.383253	−	0.663814i	−0.0121929	−	0.0211187i
$989$	6.65600	+	3.84285i	0.211649	+	0.122195i
$990$		0			0
$991$	−7.66378	−	13.2741i	−0.243448	−	0.421665i	0.718246	−	0.695789i	$-0.244945\pi$
$991$	−7.66378	−	13.2741i	−0.243448	−	0.421665i	−0.961694	+	0.274125i	$0.911612\pi$
$992$	5.87929			0.186668
$993$		0			0
$994$	−19.8590	−	7.46544i	−0.629890	−	0.236790i
$995$	−9.64089	−	5.56617i	−0.305637	−	0.176460i
$996$		0			0
$997$	−35.3852	−	20.4297i	−1.12066	−	0.647014i	−0.179092	−	0.983832i	$-0.557316\pi$
$997$	−35.3852	−	20.4297i	−1.12066	−	0.647014i	−0.941570	+	0.336818i	$0.890649\pi$
$998$	−23.8844	+	13.7897i	−0.756047	+	0.436504i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.t.b.341.11		30
3.2	odd	2		315.2.t.b.131.5	yes	30
7.3	odd	6		945.2.be.b.206.5		30
9.2	odd	6		945.2.be.b.656.5		30
9.7	even	3		315.2.be.b.236.11	yes	30
21.17	even	6		315.2.be.b.311.11	yes	30
63.38	even	6	inner	945.2.t.b.521.5		30
63.52	odd	6		315.2.t.b.101.11	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.t.b.101.11	✓	30	63.52	odd	6
315.2.t.b.131.5	yes	30	3.2	odd	2
315.2.be.b.236.11	yes	30	9.7	even	3
315.2.be.b.311.11	yes	30	21.17	even	6
945.2.t.b.341.11		30	1.1	even	1	trivial
945.2.t.b.521.5		30	63.38	even	6	inner
945.2.be.b.206.5		30	7.3	odd	6
945.2.be.b.656.5		30	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.23569i q^{2} +0.473066 q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.47654 + 0.930987i) q^{7} +3.05595i q^{8} +O(q^{10})\)	\(q+1.23569i q^{2} +0.473066 q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.47654 + 0.930987i) q^{7} +3.05595i q^{8} +(1.07014 - 0.617846i) q^{10} +(1.10058 + 0.635419i) q^{11} +(1.67710 + 0.968277i) q^{13} +(-1.15041 + 3.06024i) q^{14} -2.83008 q^{16} +(-0.676881 - 1.17239i) q^{17} +(-0.724595 - 0.418345i) q^{19} +(-0.236533 - 0.409687i) q^{20} +(-0.785182 + 1.35997i) q^{22} +(0.914519 - 0.527998i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-1.19649 + 2.07238i) q^{26} +(1.17157 + 0.440418i) q^{28} +(8.49399 - 4.90401i) q^{29} -2.24847i q^{31} +2.61479i q^{32} +(1.44872 - 0.836416i) q^{34} +(-0.432012 - 2.61024i) q^{35} +(-4.38029 + 7.58689i) q^{37} +(0.516945 - 0.895376i) q^{38} +(2.64653 - 1.52797i) q^{40} +(-3.47470 + 6.01835i) q^{41} +(3.63907 + 6.30306i) q^{43} +(0.520646 + 0.300595i) q^{44} +(0.652443 + 1.13006i) q^{46} +1.69463 q^{47} +(5.26652 + 4.61126i) q^{49} +(-1.07014 - 0.617846i) q^{50} +(0.793381 + 0.458059i) q^{52} +(0.148100 - 0.0855054i) q^{53} -1.27084i q^{55} +(-2.84505 + 7.56818i) q^{56} +(6.05984 + 10.4960i) q^{58} -9.77894 q^{59} -2.84883i q^{61} +2.77842 q^{62} -8.89123 q^{64} -1.93655i q^{65} +13.0901 q^{67} +(-0.320209 - 0.554619i) q^{68} +(3.22546 - 0.533834i) q^{70} +6.48936i q^{71} +(9.10680 - 5.25781i) q^{73} +(-9.37506 - 5.41269i) q^{74} +(-0.342781 - 0.197905i) q^{76} +(2.13406 + 2.59827i) q^{77} -16.0108 q^{79} +(1.41504 + 2.45092i) q^{80} +(-7.43683 - 4.29366i) q^{82} +(-4.56456 - 7.90605i) q^{83} +(-0.676881 + 1.17239i) q^{85} +(-7.78864 + 4.49677i) q^{86} +(-1.94181 + 3.36331i) q^{88} +(9.41641 - 16.3097i) q^{89} +(3.25197 + 3.95934i) q^{91} +(0.432628 - 0.249778i) q^{92} +2.09404i q^{94} +0.836690i q^{95} +(-8.14174 + 4.70063i) q^{97} +(-5.69810 + 6.50780i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 30 q^{4} - 15 q^{5} - 3 q^{7}+O(q^{10}) \) 30 * q - 30 * q^4 - 15 * q^5 - 3 * q^7	\( 30 q - 30 q^{4} - 15 q^{5} - 3 q^{7} + 3 q^{10} - 9 q^{11} - 12 q^{13} + 27 q^{14} + 42 q^{16} + 3 q^{17} + 15 q^{20} + 15 q^{22} - 15 q^{25} - 24 q^{26} + 27 q^{28} + 48 q^{34} + 6 q^{35} - 3 q^{37} + 30 q^{38} + 3 q^{40} + 18 q^{41} + 12 q^{43} - 15 q^{44} + 9 q^{46} + 60 q^{47} - 15 q^{49} - 3 q^{50} - 33 q^{52} + 30 q^{53} - 42 q^{56} - 30 q^{59} - 12 q^{62} - 138 q^{64} + 12 q^{67} + 21 q^{68} - 18 q^{70} + 6 q^{73} - 54 q^{74} - 54 q^{76} + 9 q^{77} + 24 q^{79} - 21 q^{80} + 6 q^{82} + 6 q^{83} + 3 q^{85} + 60 q^{86} - 48 q^{88} + 3 q^{89} + 15 q^{91} + 3 q^{92} + 36 q^{97} - 24 q^{98}+O(q^{100}) \) 30 * q - 30 * q^4 - 15 * q^5 - 3 * q^7 + 3 * q^10 - 9 * q^11 - 12 * q^13 + 27 * q^14 + 42 * q^16 + 3 * q^17 + 15 * q^20 + 15 * q^22 - 15 * q^25 - 24 * q^26 + 27 * q^28 + 48 * q^34 + 6 * q^35 - 3 * q^37 + 30 * q^38 + 3 * q^40 + 18 * q^41 + 12 * q^43 - 15 * q^44 + 9 * q^46 + 60 * q^47 - 15 * q^49 - 3 * q^50 - 33 * q^52 + 30 * q^53 - 42 * q^56 - 30 * q^59 - 12 * q^62 - 138 * q^64 + 12 * q^67 + 21 * q^68 - 18 * q^70 + 6 * q^73 - 54 * q^74 - 54 * q^76 + 9 * q^77 + 24 * q^79 - 21 * q^80 + 6 * q^82 + 6 * q^83 + 3 * q^85 + 60 * q^86 - 48 * q^88 + 3 * q^89 + 15 * q^91 + 3 * q^92 + 36 * q^97 - 24 * q^98

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